AB+BA = 1A4
In the correctly worked out addition problem above, A and B represent two different digits. What digit does A represent?
a 3
b 4
c 5
d 8
e 9
59+95=154
To determine the value of digit A in the addition problem AB + BA = 1A4, we need to follow a systematic approach.
Let's break down the addition problem and analyze it step by step:
1. We start by adding the rightmost digits, B + A. Since B and A are different digits, the sum of B and A will be a two-digit number. Therefore, the sum of B + A cannot be greater than 18 (9 + 9).
2. The rightmost digit in the sum is 4. This means that the remainder of the two-digit sum (B + A) when divided by 10 is 4.
3. Since the remainder is 4, and the sum cannot be greater than 18, the possible values of the two-digit sum (B + A) are 14 and 24.
Now, let's consider the different scenarios:
Scenario 1: If the sum (B + A) is 14:
- Since the rightmost digit in the sum is 4, the leftmost digit must be 1. Therefore, A = 1 and B = 3 (14 = B + A = 3 + 1).
Scenario 2: If the sum (B + A) is 24:
- Since the rightmost digit in the sum is 4, the leftmost digit must be 1. Therefore, A = 4 and B = 8 (24 = B + A = 8 + 4).
Based on the two scenarios, we have two possibilities for the value of A: 1 and 4. However, since A and B represent different digits, we can conclude that A cannot be equal to B. Therefore, A = 4.
Hence, the digit A represents the number 4.
Therefore, the correct answer is:
b) 4